Numerical solution for the variable order linear cable equation with Bernstein polynomials

2014 ◽  
Vol 238 ◽  
pp. 329-341 ◽  
Author(s):  
Yiming Chen ◽  
Liqing Liu ◽  
Baofeng Li ◽  
Yannan Sun
Keyword(s):  
Numerical Solution ◽  
Bernstein Polynomials ◽  
Variable Order ◽  
Cable Equation ◽  
Order Linear

scholarly journals Numerical solution of fractional variable order linear control system in state-space form

2017 ◽  
Vol 65 (5) ◽  
pp. 715-724
Author(s):  
W. Malesza ◽  
M. Macias
Keyword(s):  
Numerical Solution ◽  
State Space ◽  
Control Systems ◽  
Space Form ◽  
Linear Control ◽  
Linear Control Systems ◽  
Variable Order ◽  
Matrix Approach ◽  
Analog Model ◽  
Order Linear

Abstract The aim of this paper is to introduce a matrix approach for approximate solving of non-commensurate fractional variable order linear control systems in state-space form. The approach is based on switching schemes that realize variable order derivatives. The obtained numerical solution is compared with simulation and analog model results.

Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

2021 ◽  
Author(s):  
C. J. Zúñiga-Aguilar ◽  
J. F. Gómez-Aguilar ◽  
H. M. Romero-Ugalde ◽  
R. F. Escobar-Jiménez ◽  
G. Fernández-Anaya ◽  
...  
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Differential Equations ◽  
Numerical Solution ◽  
Variable Order ◽  
Artificial Neural

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

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